We consider refinement of finite element discretizations by splitting nodes along edges. For

this process, we derive asymptotic expansions of Galerkin solutions of linear second-order

elliptic equations. Thereby, we calculate a topological derivative w.r.t. node insertion for

functionals such as the total potential energy, minimization of which decreases the approxi-

mation error in the energy norm. Hence, these sensitivities can be used to define indicators for

local h-refinement. Our results suggest that this procedure leads to an efficient adaptive re-

finement method. This presentation is concerned with a model problem in 1d. The extension

of this concept to higher dimensions will be the subject of forthcoming publications.

},
author = {Friederich, Jan and Leugering, Günter and Steinmann, Paul},
doi = {10.1002/gamm.201210012},
faupublication = {yes},
journal = {GAMM-Mitteilungen},
note = {UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.anadap},
pages = {175-190},
peerreviewed = {unknown},
title = {{An} adaptive finite element method based on sensitivities for node insertion},
url = {http://onlinelibrary.wiley.com/doi/10.1002/gamm.201210012/full},
volume = {35},
year = {2012}
}
@article{faucris.119814024,
author = {Friederich, Jan and Pfaller, Sebastian and Steinmann, Paul},
doi = {10.1007/s00419-015-1049-9},
faupublication = {yes},
journal = {Archive of Applied Mechanics},
pages = {1-9},
peerreviewed = {Yes},
title = {{A} web-based tool for the interactive visualization of stresses in an infinite plate with an elliptical hole under simple tension: www.ltm.fau.de/plate .},
year = {2015}
}
@inproceedings{faucris.118724804,
abstract = {Structural shape optimization has become an important tool in engineering when it comes to improving components with respect to a given cost function. However, in many applications the designer has to ensure that the optimized part is still manufacturable. This work introduces two approaches on how to handle manufacturing constraints in parameter- free sensitivity-based shape optimization. In the so-called implicit method the set of design nodes is split into two groups of optimization nodes and dependent nodes. The optimization nodes are then handled as design nodes, whereas the dependent nodes are coupled to the optimization nodes in such a way that the manufacturing constraint is fulfilled. By that procedure no additional constraints have to be appended to the optimization problem. When no dependency can be determined additional equality and inequality constraints have to be formulated in terms of the coordinates of the design nodes. In this case the formulation of manufacturing constraints may lead to a large number of inequalities. Since most optimization algorithms are not able to handle highly restricted problems the use of aggregation formulations is investigated.},
author = {Schmitt, Oliver and Friederich, Jan and Steinmann, Paul},
booktitle = {Proceedings of 1st International Conference on Engineering and Applied Sciences Optimization},
date = {2014-06-04/2014-06-06},
edition = {-},
faupublication = {yes},
isbn = {978-960999946-5},
keywords = {Manufacturing constraints; Parameter-free; Sensitivity-based; Shape optimization},
note = {UnivIS-Import:2015-04-16:Pub.2014.tech.FT.FT-TM.manufa{\_}0},
pages = {2532-2542},
peerreviewed = {unknown},
publisher = {National Technical University of Athens},
title = {{Manufacturing} constraints in parameter-free sensitivity-based shape optimization},
venue = {Kos Island, Greece},
volume = {-},
year = {2014}
}
@inproceedings{faucris.118725684,
abstract = {Structural shape optimization has become an important tool for engineers when it comes to improving components with respect to a given goal function. During this process the designer has to ensure that the optimized part stays manufacturable. Depending on the manufacturing process several requirements could be relevant such as demolding or different kinds of symmetry. This work introduces two approaches on how to handle manufacturing constraints in parameter-free shape optimization. In the so–called explicit approach equality and inequality equations are formulated using the coordinates of the FE-nodes. These equations can be used to extend the optimization problem. Since the number of the additional constraint equations may be very large we apply aggregation formulations, e.g. the Kreisselmeier-Steinhauser function, if necessary. In the second approach, the so–called implicit method, the set of design nodes is split in two groups called optimization nodes and dependent nodes. The optimization nodes are now handled as design nodes but the dependent nodes are coupled to the optimization nodes in such a way that the manufacturing constraint is fulfilled. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)},
address = {Erlangen, Germany},
author = {Schmitt, Oliver and Friederich, Jan and Steinmann, Paul},
booktitle = {PAMM},
date = {2014-03-10/2014-03-14},
doi = {10.1002/pamm.201410376},
edition = {-},
faupublication = {yes},
note = {UnivIS-Import:2015-04-16:Pub.2014.tech.FT.FT-TM.manufa{\_}3},
pages = {787-788},
peerreviewed = {unknown},
publisher = {Wiley},
title = {{Manufacturing} constraints in parameter-free shape optimization},
venue = {Erlangen, Germany},
volume = {-},
year = {2014}
}
@inproceedings{faucris.121778624,
address = {Weinheim},
author = {Riehl, Stefan and Friederich, Jan and Steinmann, Paul},
booktitle = {Proc. Appl. Math. Mech.},
date = {2014-03-10/2014-03-14},
doi = {10.1002/pamm.201410375},
edition = {1},
faupublication = {yes},
note = {UnivIS-Import:2015-04-16:Pub.2014.tech.FT.FT-TM.onregu},
pages = {785-786},
publisher = {WILEY-VCH Verlag},
title = {{On} regularization in parameter-free shape optimization},
venue = {Erlangen},
volume = {14},
year = {2014}
}
@article{faucris.113964884,
author = {Riehl, Stefan and Friederich, Jan and Scherer, Michael and Meske, Ralf and Steinmann, Paul},
doi = {10.1016/j.cma.2014.05.009},
faupublication = {yes},
journal = {Computer Methods in Applied Mechanics and Engineering},
note = {UnivIS-Import:2015-03-09:Pub.2014.tech.FT.FT-TM.onthed},
pages = {119-144},
peerreviewed = {Yes},
title = {{On} the discrete variant of the traction method in parameter-free shape optimization},
volume = {278},
year = {2014}
}
@article{faucris.119753964,
abstract = {We introduce a novel method to handle geometrical and manufacturing constraints in parameter-free shape optimization. Therefore the design node coordinates are split in two sets where one set is declared as new design variables and the other set is coupled to the new design variables such that the geometrical constraint is fulfilled. Thereby no additional equations are appended to the optimization problem. In contrast the implementation of a demolding constraint is presented by formulating inequality constraints which indeed have to be attached to the optimization problem. In the context of a sensitivity–based shape optimization approachall manufacturing constraints have to be formulated in terms of the finite element node coordinates such that first order gradients with respect to the design node coordinates can be derived.}, author = {Schmitt, Oliver and Friederich, Jan and Riehl, Stefan and Steinmann, Paul}, doi = {10.1007/s00158-015-1359-0}, faupublication = {yes}, journal = {Structural and Multidisciplinary Optimization}, keywords = {shape optimization; manufacturing constraints; geometrical constraints; symmetry; parameter-free; sensitivity analysis}, pages = {881 - 892}, peerreviewed = {Yes}, title = {{On} the formulation and implementation of geometric and manufacturing constraints in node-based shape optimization}, volume = {53}, year = {2016} }